AMO 2027 Grades 9-11 SET 1 - Self-study Question 12

Mr and Mrs Hansen and their three children are to be seated at a circular table. Let $m/n$ be the probability that children A and B are seated next to one another. If $\operatorname{HCF}(m,n)=1$, find the value of $m+n$. Rotations are considered the same arrangement, but reflections can be different, as in the source figure. Assume all circular arrangements are equally likely.



Choose one option.